Lý thuyết Floquet: một công cụ hữu ích để hiểu rõ động lực học không cân bằng

Armstrong RA, McGehee R (1980) Competitive exclusion. Am Nat 115:151–170 Brassil CE (2006) Can environmental variation generate positive indirect effects in a model of shared predation? Am Nat 167:43–54 Caswell H (2001) Matrix population models: construction, analysis, and interpretation, 2nd edn. Sinauer, Sunderland Chesson P (1994) Multispecies competition in variable environments. Theor Popul Biol 45:227–276 DeAngelis DL, Waterhouse JC (1987) Equilibrium and nonequilibrium conepts in ecological models. Ecol Monogr 57:1–21 Dhooge A, Govaerts W, Kuznetsov YuA (2003) MatCont: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans Math Softw 29:141–164 Doedel EJ, Paffenroth RC, Champneys AR, Fairgrieve TF, Kuznetsov YuA, Oldeman BE, Sandstede B, Wang XJ (2001) AUTO2000: continuation and bifurcation software for ordinary differential equations. https://sourceforge.net/projects/auto2000/ Drazin PG (1992) Nonlinear systems. Cambridge University Press, Cambridge Ermentrout B (2002) Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. SIAM, Philadelphia. Ferriere R, Gatto M (1995) Lyapunov exponents and the mathematics of invasion in oscillatory or chaotic populations. Theor Popul Biol 48:126–171 Gonzalez A, Holt RD (2002) The inflationary effects of environmental fluctuations in source-sink systems. Proc Natl Acad Sci U S A 99:14872–14877 Gökçek C (2004) Stability analysis of periodically switched linear systems using Floquet theory. Math Probl Eng 2004:1–10 Grimshaw R (1993) Nonlinear ordinary differential equations. CRC, Ann Arbor Grover JP (1990) Resource competition in a variable environment: phytoplankton growing according to Monod’s model. Am Nat 136:771–789 Grover JP (1991) Resource competition in a variable environment: phytoplankton growing according to the variable-internal-stores model. Am Nat 138:811–835 Grover JP, Holt RD (1998) Disentangling resource and apparent competition: realistic models for plant-herbivore communities. J Theor Biol 191:353–376 Hastings A (1997) Population biology: concepts and models. Springer, Berlin Heidelberg New York Hastings A, Powell T (1991) Chaos in a three-species food chain. Ecology 72:896–903 Holt RD, Barfield M, Gonzalez A (2003) Impacts of environmental variability in open populations and communities: “inflation” in sink environments. Theor Popul Biol 64: 315–330 Kaitala V, Lundberg P, Ripa J, Ylikarjula J (1997) Red blue and green: dyeing population dynamics. Ann Zool Fenn 34:217–228 Koch AL (1974) Competition coexistence of two predators utilizing the same prey under constant environmental conditions. J Theor Biol 44:387–395 Kooi BW, Troost TA (2006) Advantage of storage in a fluctuating environment. Theor Popul Biol 70:527–541 Kratz TK, Deegan LA, Harmon ME, Lauenroth WK (2003) Ecological variability in space and time: insights gained from the US LTER program. BioScience 53:57–67 Kuznetsov YuA, Levitin VV (1996) CONTENT: a multiplatform environment for analyzing dynamical systems. Dynamical Systems Laboratory, Centrum voor Wiskunde en Informatica, Amsterdam. http://www.math.uu.nl/people/kuznet/CONTENT/ Kuznetsov YuA, Rinaldi, S (1996) Remarks on food chain dynamics. Math Biosci 134:1–33 Levin SA (1970) Community equilibria and stability, and an extension of the competitive exclusion principle. Am Nat 104:413–423 Litchman E, Klausmeier CA (2001) Competition of phytoplankton under fluctuating light. Am Nat 157:170–187 MacArthur RH, Wilson EO (1967) The theory of island biogeography. Princeton University Press, Princeton May RM (1974) Stability and complexity in model ecosystems, 2nd edn. Princeton University Press, Princeton Metz JAJ, Diekmann O (eds) (1986) The dynamics of physiologically structured populations. Springer, Berlin Heidelberg New York Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define “fitness” for general ecological scenarios? Trends Ecol Evol 7:198–202 Mylius SD, Diekmann O (2001) The resident strikes back: invader-induced switching of resident attractor. J Theor Biol 211:297–311 Namba T, Takahashi S (1993) Competitive coexistence in a seasonally fluctuating environment. II. Multiple stable states and invasion success. Theor Popul Biol 44:374–402 Nisbet RM, Gurney WSC (1982) Modelling fluctuating populations. Wiley, New York Revilla TA (2000) Resource competition in stage-structured populations. J Theor Biol 204:289–298 Roy M, Holt RD, Barfield M (2005) Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks. Am Nat 166:246–261 Steele JH, Henderson EW (1984) Modeling long-term fluctuations in fish stocks. Science 224:985–987 Strogatz SH (1994) Nonlinear dynamics and chaos. Westview, Cambridge Thoreau HD (1854) Walden; or, life in the woods. Penguin, New York Tilman D (1982) Resource competition and community structure. Princeton University Press, Princeton Tilman D, Kareiva P (eds) (1997) Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton. van Coller, L (1997) Automated techniques for the qualitative analysis of ecological models: continuous models. Conserv Ecol 1:5. http://www.consecol.org/vol1/iss1/art5/ Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317 Wolfram Research, Inc. (2007) Mathematica, version 6.0. Wolfram, Champaign Yodzis P (1989) Introduction to theoretical ecology. Harper and Row, New York